Package 'twingp'

A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling

Description

For further details on the methodology, please refer to Vakayil and Joseph (2024). The package uses nlopt (Johnson, 2007) C++ library for hyperparameter optimization, nanoflann (Blanco and Rai, 2014) C++ library for nearest neighbor queries, and Eigen (Guennebaud and Jacob, 2010) C++ library for matrix operations.

References

Vakayil, A., & Joseph, V. R. (2024). A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling. Technometrics, 66(2), 295-305.

Johnson, S. G. (2007), The NLopt nonlinear-optimization package. http://github.com/stevengj/nlopt

Guennebaud, G., Jacob, B., & Others. (2010). Eigen v3. http://eigen.tuxfamily.org

Blanco, J. L. & Rai, P. K. (2014). nanoflann: a C++ header-only fork of FLANN, a library for nearest neighbor (NN) with kd-trees. https://github.com/jlblancoc/nanoflann

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A Fast Global-Local Gaussian Process Approximation

Description

A Fast Global-Local Gaussian Process Approximation

Usage

twingp(
  x,
  y,
  x_test,
  nugget = TRUE,
  twins = 5,
  g_num = NULL,
  l_num = NULL,
  v_num = NULL,
  num_threads = NULL
)

Arguments

x	n * d numeric matrix representing the training features
y	n * 1 response vector corresponding to x
x_test	t * d numeric matrix representing the t testing locations
nugget	Boolean indicating if a nugget to model observation noise is included in the model, the default is True
twins	Number of twinning samples computed to identify the best set of global points, the default is 5
g_num	Number of global points included in the model, the default is min(50 * d, max(sqrt(n), 10 * d))
l_num	Number of local points included in the model, the default is max(25, 3 * d)
v_num	Number of validation points, the default is 2 * g_num
num_threads	Number of threads for parallel computation, the default is all available threads

Details

We employ a combined global-local approach in building the Gaussian process approximation. Our framework uses a subset-of-data approach where the subset is a union of a set of global points designed to capture the global trend in the data, and a set of local points specific to a given testing location. We use Twinning (Vakayil and Joseph, 2022) to identify the set of global points. The local points are identified as the nearest neighbors to the testing location. The correlation function is also modeled as a combination of a global, and a local kernel. For further details on the methodology, please refer to Vakayil and Joseph (2024).

Value

A list of two t * 1 vectors mu, and sigma representing the mean prediction and associated standard error corresponding to x_test

References

Vakayil, A., & Joseph, V. R. (2024). A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling. Technometrics, 66(2), 295-305.

Vakayil, A., & Joseph, V. R. (2022). Data Twinning. Statistical Analysis and Data Mining: The ASA Data Science Journal, 15(5), 598-610.

Examples

grlee12 = function(x) {
  term1 = sin(10 * pi * x) / (2 * x)
  term2 = (x - 1)^4
  y = term1 + term2
  return(y)
}

x = matrix(seq(0.5, 2.5, length=500), ncol=1)
y = apply(x, 1, grlee12) + rnorm(nrow(x)) * 0.1
x_test = matrix(seq(0.5, 2.5, length=2000), ncol=1)
y_test = apply(x_test, 1, grlee12)

result = twingp(x, y, x_test, num_threads=2)
rmse = sqrt(mean((y_test - result$mu)^2))

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